Unveiling Gargantua: A new search strategy for the most massive central cluster black holes

We aim to unveil the most massive central cluster black holes in the universe. We present a new search strategy which is based on a black hole mass gain sensitive 'calorimeter' and which links the innermost stellar density profile of a galaxy to the adiabatic growth of its central SMBH. In a first step we convert observationally inferred feedback powers into SMBH growth rates by using reasonable energy conversion efficiency parameters, $\epsilon$. In the main part of this paper we use these black hole growth rates, sorted in logarithmically increasing steps encompassing our whole parameter space, to conduct $N$-Body computations of brightest cluster galaxies with the newly developed MUESLI software. For the initial setup of galaxies we use core-Sersic models in order to account for SMBH scouring. We find that adiabatically driven core re-growth is significant at the highest accretion rates. As a result, the most massive black holes should be located in BCGs with less pronounced cores when compared to the predictions of empirical scaling relations which are usually calibrated in less extreme environments. For efficiency parameters $\epsilon<0.1$, BCGs in the most massive, relaxed and X-ray luminous galaxy clusters might even develop steeply rising density cusps. Finally, we discuss several promising candidates for follow up investigations, among them the nuclear black hole in the Phoenix cluster. Based on our results, it might have a mass of the order of $10^{11} M_\odot$.